The temperature (in ) inside a metal rod at time minutes is given by .

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

The temperature TT (in ∘ ⁣C^{\circ}\!\mathrm{C}) inside a metal rod at time tt minutes is given by T(t)=4t2−2t+3sin⁡tT(t)=4t^{2}-2t+3\sin t. (a) Determine T(π6)T\bigl(\tfrac{\pi}{6}\bigr) and T(π3)T\bigl(\tfrac{\pi}{3}\bigr). (b) Find the average rate of change of temperature over the interval [π6,π3]\bigl[\tfrac{\pi}{6},\tfrac{\pi}{3}\bigr] and state appropriate units. (c) Decide whether the temperature is rising faster or slower than 0.5 ∘ ⁣C0.5\,^{\circ}\!\mathrm{C} per minute on this interval, justifying your answer using the value obtained in part (b).

Related theory

Browse the problem library